Hilbert Space in Quantum Mechanics

[klen]

in quantum mechanics we have something called hilbert space. What does the dimensions of this space represent for that system?
also is ψ(x) same as |ψ> in the dirac notation?

 

[bhobba]

The dimension gives the number of possible outcomes of an observation. If infinite dimensional it's countably infinite but the possible outcomes can either be countably infinite or a continuum.

ψ(x) is the representation of |ψ> in terms of the eigenvectors of the position operator.

If that doesn't make sense you really need to learn about vector spaces and the Dirac notation:
http://en.wikipedia.org/wiki/Bra–ket_notation

Thanks
Bill

 

[sulbash]

The dimension gives the number of possible behavior of particle, with regards to it directions.
ψ(x) is the representation of scalar and as well |ψ> in terms of the eigenvectors of the position operator. but in the Dirac notation their are both Spinor in terms of matrices . one ψ(x)_[1] consists of two up spin and the other ψ(x)_[2]consists of two spin downward..